"It is too early for us to give you an accurate picture of what 120 lines of inquiry will distil down to but we believe we will come up with between 20 to 25 victims."

Mr Spindler said they are working to identify anyone who could be subject to criminal investigation. The BBC is not being investigated, he said.

Asked if allegations related to any institutions other than those mentioned in previous claims - the BBC, the Jersey children's home, or the school in Staines - he said he had contacted Stoke Mandeville Hospital, and Leeds Royal Infirmary.

"The pattern of his offending behaviour does appear to be on a national scale," he said.

Mr Spindler said police will produce a joint report with the NSPCC to look to see what lessons can be learned and what conclusions can be drawn, which can be shared with other agencies.

Calling it an "assessment", rather than an investigation, he said it is being carried out by Scotland Yard and being led by its Serious Case Team, which looks at complex and history cases.

There are seven officers working on the case, but that will go up to 10 tomorrow, "because we are keen to draw this to a swift conclusion", he said.

Mr Spindler said a provisional search of Scotland Yard's records could not find any record of any previous investigation into Savile, and they were only previously aware of the involvement of Surrey Police.

Although it is in its early stages, he said allegations suggested Savile's "predilection for teenage girls".

"There is a pattern of behaviour that is being presented to us which ultimately we will hope to analyse and present in a final report in some weeks time," he said.

Peter Liver, from the NSPCC, said over the last five days the charity has received 40 calls following the claims of abuse committed by Savile.

Of these, 24 have been referred to police or other agencies that can support victims of abuse, he said, and 17 directly relate to Savile.

Mr Liver said there were also 21 unrelated calls to the helpline that stemmed from publicity over the allegations.

He said they consisted of "people coming forward to report abuse as a result of the attention that has been drawn to this".

Mr Spindler said he hopes to bring the inquiry, dubbed Operation Yewtree, to as swift a conclusion as possible.

He said they will only launch investigations into living individuals about whom allegations are made if they get some evidence, which is most likely to come from witness statements.

"We are getting a range of different names reported to us, but the only allegations we have recorded are against Savile himself," he said.

He said information had been passed to Scotland Yard by the BBC's internal investigations unit, adding: "I have been in contact with the director general a number of times and agreed that they will hold back launching their own investigation until we have finished processing the material we have got.

"I am very satisfied with the level of support the BBC have provided. They are fully co-operating and I have no concerns whatsoever with the fact we can work with them."

Mr Spindler said victims would be looking for an "acknowledgement and a recognition of what happened to them."

Both he and Mr Liver paid tribute to people who had come forward.

"You really shouldn't underestimate the impact even after so many years of reliving these experiences and then to watch the public debate unfold and it has been quite significant," he said.

"It will be traumatic for some, if not all, of them.".

Mr Liver added: "I just want to acknowledge the bravery of the victims of abuse that have come forward as a result of this inquiry."

Savile's family are to remove his headstone from his grave in Scarborough, North Yorkshire.

In a statement they said: "The family members are deeply aware of the impact that the stone remaining there could have on the dignity and sanctity of the cemetery.

"Out of respect to public opinion, to those who are buried there, and to those who tend their graves and visit there, we have decided to remove it."

The grave has been targeted by vandals - a bottle was thrown at it last week, but it was not damaged, North Yorkshire Police said.